Do US Supreme Court Justices have to be reelected periodically?

They are never elected nor are they re-confirmed. The US Supreme Court Justices are appointed for life. They are nominated by the President and then confirmed by the U S Senate.

On the other hand, state supreme court justices often have term limitations. In those states where justices are elected or reconfirmed periodically, the reelection process is instituted because justices may be eligible to serve multiple terms, and are placed on the court by general election.